Find the Z scores that separate the middle 27% of the distribution from the area in the tails of the standard normal distribution

Z - score is a statistical tool that is used to determine the probability of finding a number or a value under a normal distribution plot. A normal distribution assumes that the mean is equal to zero and that the standard deviation is equal to 1. Using the z-score table, we can find the probability either on the right side or the left side. Using the table hence, we find the probability to the left of the value. The probability that is equivalent to the unknown z should be equal to 0.5 + (0.27/2) = 0.635. 0.5 comes from the assumption that the area under the curve on each side is 50% of the total. The equivalent z score is equal to z = 0.345.